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Duke University Press, Banach Journal of Mathematical Analysis, 2(6), p. 132-158

DOI: 10.15352/bjma/1342210165

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Bounds for the ratio of two gamma functions---From Wendel's and related inequalities to logarithmically completely monotonic functions

Journal article published in 2012 by Qiu-Ming Luo, Feng Qi ORCID
This paper is available in a repository.
This paper is available in a repository.

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Abstract

In the survey paper, along one of several main lines of bounding the ratio of two gamma functions, the authors retrospect and analyse Wendel's double inequality, Kazarinoff's refinement of Wallis' formula, Watson's monotonicity, Gautschi's double inequality, Kershaw's first double inequality, and the (logarithmically) complete monotonicity results of functions involving ratios of two gamma or $q$-gamma functions obtained by Bustoz, Ismail, Lorch, Muldoon, and other mathematicians.